+0  
 
0
38
1
avatar+15 

Let z be a complex number such that

 

z + 1/z = 1


Find 

 

z^3

 Oct 6, 2023
 #1
avatar+624 
0

Squaring both sides of the equation z+1/z=1, we get [z^2 + 2 + \frac{1}{z^2} = 1,]so z2+1/z2=−1. Then (z+1/z)(z2+1/z2)=(z+1/z)(−1)=−1, so z3+1=−1, so z3=−2​.

 Oct 6, 2023

2 Online Users